Artificial resonant structures known as split ring resonators (SRRs) can be designed to produce a negative effective magnetic permeability μeff in a fixed, narrow frequency band. A circuit made of a conducting trace or wire with a gap will operate analogously to a resonant circuit consisting of a resistor (R), an inductor (L), and a capacitor (C)—i.e., an RLC circuit. The physical dimension, “a,” of the circuit typically is such that a<<λ, where λ is the wavelength of the subject electromagnetic radiation of interest.
Periodic arrays of SRRs have been combined with periodic arrays of straight wires to yield an effective electric permittivity ∈eff (dielectric constant) that can be engineered to have specific values in a frequency band of interest. The quantities μeff and ∈eff are the relative permeability and permittivity—the actual values are obtained by multiplying μeff and ∈eff by the vacuum values of μ0 and ∈0 respectively. The combined effective permittivity and permeability result in an effective index of refraction, neff, where neff=(μeff∈eff)1/2, that can possess values not found in naturally occurring materials or blends of naturally occurring materials. In particular, if μeff and ∈eff are both negative then neff will be negative.
Materials having a negative neff are referred to as “left-handed materials” (LHM) or negative index materials (NIM). A NIM has some remarkable properties. For example, in a NIM the direction of refraction is opposite that of normal materials and the Doppler effect shifts frequencies in the opposite direction compared to normal materials. A NIM is one particular example of an engineered electromagnetic material, but other examples exist. Such engineered electromagnetic materials are referred to as electromagnetic “metamaterials.” Metamaterials are designed to have properties that are not found in the constituent materials and are not typically found in nature. The special electromagnetic properties of the metamaterial result mainly from its geometrical structure.
It is desirable to make an effective metamaterial that can be actively tunable with values of effective magnetic permeability and permittivity not achievable by other methods or materials. It also is desirable to make an effective metamaterial that can be employed in a wide range of device applications and over a wide range of subject electromagnetic radiation frequencies.